Abstract

In arguments made about the paradoxes of Zeno of Elea there is not always a clear distinction between attempts to determine what Zeno was originally trying to argue and how Zeno’s arguments have influenced, or been used in, modern mathematics.

In this Dissertation it is argued that if one is interested in determining the original purpose of Zeno’s arguments, then it is not helpful to either express the paradoxes as modern mathematical problems or pose modern mathematical solutions to them. Doing either of these things will adversely effect the way in which Zeno’s paradoxes can be interpreted. To the extent that Zeno’s paradoxes are discussed in modern mathematics they are usually used merely as analogies, where the question of what Zeno was originally trying to argue is largely irrelevant. This is not to say that modern mathematical argument about Zeno should not be discussed, simply that they are a different set of arguments. If one is trying to determine Zeno’s original argument then one should focus instead on analysing the arguments made against Zeno by other ancient thinkers. Ancient thinkers are likely to have had a far better understanding of Zeno’s original argument simply because they are historically closer to him.

This dissertation discusses two articles in which this issue arises. In neither article is it claimed that Zeno’s paradoxes were simple statements of mathematical fallacy. However, both authors insist on comparing the arguments which Zeno and his ancient opponent appear to make, with modern mathematical arguments. This obscures certain ways of interpreting Zeno’s paradoxes. An interpretation of Zeno’s argument, which is likely to be overlooked if a modern approach to Zeno is taken, will be discussed in this dissertation.

A mathematical approach to Zeno can obscure the possibility that Zeno might have been more interested in the question of how it is possible that an extension can have the infinite number of extended parts which it appears to have. A mathematical approach to Zeno tends to focus more on infinite summation and infinite amounts in a purely abstract and non-physical sense.